Solution to the n-bubble problem on $$\mathbb {R}^1$$ with log-concave density-Reference-Cited by-同舟云学术

Solution to the n-bubble problem on $$\mathbb {R}^1$$ with log-concave density

Published:2023-09-28 Issue:3 Volume:64 Page:
ISSN:0232-704X
Container-title:Annals of Global Analysis and Geometry
language:en
Short-container-title:Ann Glob Anal Geom

Author:

Ross John

Abstract

AbstractWe study the n-bubble problem on

$$\mathbb {R}^1$$

R 1 with a prescribed density function f that is even, radially increasing, and satisfies a log-concavity requirement. Under these conditions, we find that isoperimetric solutions can be identified for an arbitrary number of regions, and that these solutions have a well-understood and regular structure. This generalizes recent work done on the density function

$$|x |^p$$

| x | p and stands in contrast to log-convex density functions which are known to have no such regular structure.

Funder

Southwestern University

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s10455-023-09927-8.pdf

Reference14 articles.

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